6. Normal Distribution and Continuous Random Variables

Which of the following is a property of the standard normal distribution?

Suppose $X$ is a standard normal random variable with density function $f\left(x\right)$. What is the value of $P(1<X<4)$?

Given a standard normal variable $z$, what is the value of $P(z<0)$?

For the standard normal distribution, what is the probability that $0.6\le z\le 2.12$? Choose the closest value.

Which of the following best describes the shaded region on a standard normal distribution curve that corresponds to the probability $P(a<z<b)$?

If Cynthia's test score is $1.5$ standard deviations above the mean, what is her $z$-score in the standard normal distribution?

Which of the following accurately describes the proportions in the tails of a standard normal distribution?

In the $SND$ (standard normal distribution), what happens to the graph of the normal curve as the mean $\mu$ increases while the standard deviation $\sigma$ remains constant?

For the standard normal distribution, what is the area under the curve to the left of $z=1$?

Which of the following does not describe the standard normal distribution?

Using the standard normal table, what is the probability that $z\ge 1.4$? Round your answer to the nearest percent.

Which of the following does not describe the standard normal distribution?

The standard normal curve is associated with which normal distribution?

In Exercises 8 and 9, assume that women have standing eye heights that are normally distributed with a mean of 59.7 in. and a standard deviation of 2.5 in. (based on anthropometric survey data from Gordon, Churchill, et al.).

a. If an eye recognition security system is positioned at a height that is uncomfortable for women with standing eye heights less than 54 in., what percentage of women will find that height uncomfortable?

Which of the following is true regarding the standard normal distribution?